This is a rush transcript from "Your World," April 24, 2013. This copy may not be in its final form and may be updated.

NEIL CAVUTO, HOST: After the bombing, now the rethinking. And suddenly an immigration reform plan that looked ready for takeoff now looks increasingly all but off.

Florida Senator Marco Rubio says that would be a shame because the bill he and fellow Gang of 8 pounded out pounds out the very problems and criticisms illegal immigration folks have been sort of railing against ever since Boston.

The senator joins me now.

Senator, very good to have you.

SEN. MARCO RUBIO, R-FLA.: Thank you.

CAVUTO: I guess what comes back -- and I have talked to a few of them -- in fact, I'm going to replay a couple of their comments, sir -- is that the enforcement provision and further cracking down on the bad guys who might already be here. What do you say?

RUBIO: Right.

Well, first of all, the bill was never designed as a "take it or leave it" proposition. It's a starting point. And I would just say that I share that concern. Look, the fundamental challenge we have here is that no one believes this administration is serious about enforcing the laws.

If people thought the administration was serious about enforcing immigration laws, this debate would be a lot simpler. And so we need to figure out a way to guarantee in the law that the law will be enforced, that border will be secured, et cetera.

And what I'm saying is, this bill is a starting point for that discussion. And so if somebody out there or my colleagues have an idea about how we can guarantee that the laws are enforced, then let's do it. We're open to that. And hopefully that's what we will get here from this open and significant process that I hope we will undergo. We think we have a good starting point. We think we can build on it. And we hope that we will.

CAVUTO: Are you worried post-Boston, though, that it's going to make it tougher?

RUBIO: Yes.

Oh, well, listen, if Boston exposes flaws in our system, immigration or otherwise, we should address that and we should address that in this bill, if possible, of course. That's one of the things the bill does. It requires people that are illegally here to undergo a background check and a national security check and maybe that should be expanded for everybody, visitors, et cetera.

The point is we're open to those sorts of things. Why would you have a tragedy happen in Boston, which was horrible, but we need to learn from it, and why would you not apply those lessons, whether it's in this bill or some other bill?

CAVUTO: Do you think they have piled on too much to this bill then in hopes that it will address not only the illegals who are here, but they want to expand or some do the legals who are here, or those who have been granted visas or recently citizenship, as in the case of these two brothers in Boston?

That then gets into another whole area that goes well beyond what you were trying to do with this package. Right?

RUBIO: Well, first of all, just remember we have one million people a year coming permanently and legally. These were two people and they both came as children. We need to learn a lot more about what happened there, but let's keep that in perspective.

And if there's something that went wrong in the process, the asylum process, the refugee process, let's fix it. We should fix it. We're always in the process of learning and applying lessons here, just like America...

CAVUTO: But don't you think that that is what is going to slow this down, Senator?

RUBIO: It might.

CAVUTO: They're going to say, if we have to go much slower and then examine each and everyone who is here, and in the future how we will allow them here and assimilate them here, then it will take a lot longer than even you planned?

RUBIO: Well, you mean the bill or the process for allowing people in?

CAVUTO: I mean both actually.

RUBIO: Yes.

Well, for the bill, I don't have a problem with that. I have never said this has to be done quickly. This country has been struggling with this for three decades. Let's do it right so we don't have to do it again. And I have always said that. That's why I want this to be a significant process.

And the Senate, we're still in -- they haven't even starting working on it in the committee yet. As far as the immigration process is concerned, look, the immigration process, first and foremost must be good for America. My point is if there's ways to improve it, we should do it, no matter what it is that leads us to learn those lessons.

But I think that having 11 million people here illegally, not knowing who they are or why there here or where they are, that is not good for us either. And we have to address that, because if we do nothing, let's say this thing falls apart, then we're stuck with is what we have now and what we have now is terrible. I'm not sure who benefits from what we have now, but it certainly isn't America.

CAVUTO: When you look at what has happened post-Boston, Senator, there's been this sort of collective angst in Washington how to address future such Bostons. Maybe we have to up our security, increase our drones.

Senator Rand Paul was here sort of dialing back at least to me what was the thrust of his filibuster by saying it's OK to use this technology to go -- I think I'm quoting him right -- after bad guys, but limit it on good guys. That, I understood.

But it seemed to send a mixed message to folks, that Republicans are either for or against these things. Where do you stand?

RUBIO: Well, first of all, this is the -- just like after 9/11, America hasn't been the same. It won't be the same after Boston.

We still have terrorist cells around the world planning to attack us, but increasingly we're finding and learning about homegrown elements, people that were born and raised here and people that immigrated here as children, what have you, that have been radicalized even though they have never visited abroad.

They have been radicalized on the Internet. And the result is we have to deal with that reality as well. Our national security -- my problem with this administration is they refuse to acknowledge the existence of this kind of terrorism. They do everything they can to avoid calling it terrorism. That's why you have the situation with Benghazi.

And even now -- irrespective of whether these guys met with extremists or not when they went to Russia, the bottom line is they were radicalized. And they carried out an attack because of that ideology. This is the emerging face of terrorism across -- against the United States by radical Islamists. And we have to have security systems that recognize that and can deal with that, because the number one job of the federal government is to secure our national security.

CAVUTO: I can understand that, as I understood what Senator Rand Paul was telling me, but you can't filibuster against this sort of thing because you think it's too intrusive, and then use this technology when you think it could be warranted.

RUBIO: Right.

CAVUTO: Isn't that essentially the administration's position?

RUBIO: Well, first of all, I think the problem with the administration and the filibuster -- and I actually have disagreements with Senator Paul about drone policy -- what I agreed with is that he deserved an answer to his question.